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A uniform heavy rod of weight W, cross s...

A uniform heavy rod of weight W, cross sectional area a and length L is hanging from fixed support. Young modulus of the material of the rod is Y. Neglect the lateral contraction. Find the elongation of the rod.

A

`(1)/(2) (WL)/(YA)`

B

`(1)/(3) (WL)/(YA)`

C

`2(WL)/(YA)`

D

`3(WL)/(YA)`

Text Solution

Verified by Experts

The correct Answer is:
A
The stress at the position of this element is produced by the weight of the lod of length `x` lying below it, ie.., `(W//L)x`. Therefore, stress at this section
`sigma = ((W//L)x)/(A) = (Wx)/(Al)`
The elongation produced in the rod can be calculated as `delta = int d delta`
`delta = (W)/(YAL) int_(0)^(L) xdx = (W)/(YAL) [(x^(2))/(2)]_(0)^(L)` or `sigma = (1)/(2) (WL)/(YA)`
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